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We calculate the exclusive $\mathrm{J}/\psi$ photoproduction cross section athigh energies from the Color Glass Condensate approach. The results arecompared to the center-of-mass energy dependent $\gamma+A\to\mathrm{J}/\psi+A$cross sections extracted from measurements in ultra peripheral heavy ioncollisions at RHIC and LHC. We predict strong saturation-driven nuclearsuppression at high energies, while LHC data prefers even stronger suppression.We explore the effect of nucleon shape fluctuations on the nuclear suppressionin the coherent and incoherent cross sections, and show that the most recentmeasurement of the $|t|$-differential incoherent $\mathrm{J}/\psi$ crosssection prefers large event-by-event fluctuations of the nucleon substructurein heavy nuclei, comparable to that found for a free proton.

Energy dependent nuclear suppression from gluon saturation in exclusive vector meson production